12a
0203
(K12a
0203
)
A knot diagram
1
Linearized knot diagam
3 6 7 8 10 2 1 11 12 5 9 4
Solving Sequence
2,7
6 3 4 1
8,10
5 11 12 9
c
6
c
2
c
3
c
1
c
7
c
5
c
10
c
12
c
9
c
4
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= hu
99
+ u
98
+ ··· + b − u, −u
99
+ u
98
+ ··· − 2u
2
+ a, u
101
− 2u
100
+ ··· − 3u + 1i
I
u
2
= hb + u, −u
3
+ a − u + 1, u
4
+ u
2
− u + 1i
I
u
3
= h−u
5
− u
4
− 2u
3
− 2u
2
+ b − 2u − 1, u
4
+ u
2
+ a, u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1i
* 3 irreducible components of dim
C
= 0, with total 111 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I.
I
u
1
= hu
99
+u
98
+· · ·+b−u, −u
99
+u
98
+· · ·−2u
2
+a, u
101
−2u
100
+· · ·−3u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
u
8
+ u
6
+ u
4
+ 1
u
10
+ 2u
8
+ 3u
6
+ 2u
4
+ u
2
a
10
=
u
99
− u
98
+ ··· − 4u
3
+ 2u
2
−u
99
− u
98
+ ··· − 3u
2
+ u
a
5
=
u
21
+ 4u
19
+ 9u
17
+ 12u
15
+ 12u
13
+ 10u
11
+ 9u
9
+ 6u
7
+ 3u
5
+ u
u
23
+ 5u
21
+ ··· + 2u
3
+ u
a
11
=
−u
99
+ u
98
+ ··· + 2u − 1
u
99
− u
98
+ ··· + 2u
3
− 2u
2
a
12
=
−u
11
− 2u
9
− 2u
7
+ u
3
u
11
+ 3u
9
+ 4u
7
+ 3u
5
+ u
3
+ u
a
9
=
−u
96
+ u
95
+ ··· − 2u
3
+ u
−u
98
+ u
97
+ ··· − 2u
2
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4u
100
+ 12u
99
+ ··· − 27u + 14
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
101
+ 48u
100
+ ··· + u − 1
c
2
, c
6
u
101
− 2u
100
+ ··· − 3u + 1
c
3
u
101
+ 2u
100
+ ··· + 12760u + 1480
c
4
u
101
− 2u
100
+ ··· − 86401u + 194329
c
5
, c
10
u
101
− u
100
+ ··· − 1024u − 1024
c
7
u
101
− 10u
100
+ ··· − 42087u + 6643
c
8
, c
9
, c
11
u
101
+ 11u
100
+ ··· − 8u − 1
c
12
u
101
+ 12u
100
+ ··· + 3723u + 277
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
101
+ 12y
100
+ ··· − 7y −1
c
2
, c
6
y
101
+ 48y
100
+ ··· + y −1
c
3
y
101
− 24y
100
+ ··· + 111920400y −2190400
c
4
y
101
− 48y
100
+ ··· − 26966856735y −37763760241
c
5
, c
10
y
101
+ 63y
100
+ ··· − 4718592y −1048576
c
7
y
101
+ 24y
100
+ ··· − 2017745343y −44129449
c
8
, c
9
, c
11
y
101
− 99y
100
+ ··· − 132y
2
− 1
c
12
y
101
+ 12y
100
+ ··· + 194657y −76729
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.559286 + 0.752293I
a = −0.989959 + 0.356199I
b = −0.100806 + 0.217494I
5.04653 + 2.23098I 0
u = 0.559286 − 0.752293I
a = −0.989959 − 0.356199I
b = −0.100806 − 0.217494I
5.04653 − 2.23098I 0
u = 0.144841 + 1.062320I
a = −0.49301 + 1.46252I
b = −0.244757 − 0.364265I
6.80947 + 2.51778I 0
u = 0.144841 − 1.062320I
a = −0.49301 − 1.46252I
b = −0.244757 + 0.364265I
6.80947 − 2.51778I 0
u = −0.675241 + 0.627440I
a = 1.51592 − 1.43887I
b = −0.516038 + 0.020363I
10.7524 − 9.3652I 0
u = −0.675241 − 0.627440I
a = 1.51592 + 1.43887I
b = −0.516038 − 0.020363I
10.7524 + 9.3652I 0
u = 0.223863 + 1.080890I
a = −0.486349 − 0.383572I
b = 0.666393 − 0.872846I
−0.470150 + 0.026524I 0
u = 0.223863 − 1.080890I
a = −0.486349 + 0.383572I
b = 0.666393 + 0.872846I
−0.470150 − 0.026524I 0
u = −0.656822 + 0.605840I
a = −1.30126 + 1.72034I
b = 0.938922 − 0.038188I
4.32173 − 5.33553I 0
u = −0.656822 − 0.605840I
a = −1.30126 − 1.72034I
b = 0.938922 + 0.038188I
4.32173 + 5.33553I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.329615 + 1.062400I
a = 1.384260 + 0.126784I
b = −1.230950 + 0.038847I
−1.42344 + 0.99591I 0
u = 0.329615 − 1.062400I
a = 1.384260 − 0.126784I
b = −1.230950 − 0.038847I
−1.42344 − 0.99591I 0
u = −0.698021 + 0.546127I
a = −0.496542 + 1.163010I
b = 1.20205 − 0.87188I
12.26350 + 2.91510I 11.73744 + 0.I
u = −0.698021 − 0.546127I
a = −0.496542 − 1.163010I
b = 1.20205 + 0.87188I
12.26350 − 2.91510I 11.73744 + 0.I
u = 0.660879 + 0.588204I
a = −0.080340 + 0.833596I
b = 0.561946 + 0.166495I
6.75246 + 2.85123I 9.64304 + 0.I
u = 0.660879 − 0.588204I
a = −0.080340 − 0.833596I
b = 0.561946 − 0.166495I
6.75246 − 2.85123I 9.64304 + 0.I
u = 0.517354 + 0.988210I
a = 0.364633 + 0.337762I
b = −0.0884803 + 0.0436767I
0.07186 + 2.63242I 0
u = 0.517354 − 0.988210I
a = 0.364633 − 0.337762I
b = −0.0884803 − 0.0436767I
0.07186 − 2.63242I 0
u = −0.591512 + 0.946011I
a = 0.292258 − 0.036431I
b = −0.782515 + 1.097640I
9.81181 + 4.46013I 0
u = −0.591512 − 0.946011I
a = 0.292258 + 0.036431I
b = −0.782515 − 1.097640I
9.81181 − 4.46013I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.570523 + 0.963388I
a = −0.350315 + 0.737669I
b = 1.32634 − 1.23936I
3.26846 + 0.54908I 0
u = −0.570523 − 0.963388I
a = −0.350315 − 0.737669I
b = 1.32634 + 1.23936I
3.26846 − 0.54908I 0
u = −0.216987 + 1.103730I
a = −2.37752 − 0.70582I
b = 1.28080 + 1.71958I
1.05599 + 2.54758I 0
u = −0.216987 − 1.103730I
a = −2.37752 + 0.70582I
b = 1.28080 − 1.71958I
1.05599 − 2.54758I 0
u = −0.657710 + 0.567007I
a = 0.71084 − 1.74178I
b = −1.275050 + 0.427296I
4.96120 − 0.22906I 9.98542 + 0.I
u = −0.657710 − 0.567007I
a = 0.71084 + 1.74178I
b = −1.275050 − 0.427296I
4.96120 + 0.22906I 9.98542 + 0.I
u = 0.573003 + 0.978593I
a = −0.711923 − 0.889848I
b = 0.225706 − 0.133500I
5.60153 + 1.95285I 0
u = 0.573003 − 0.978593I
a = −0.711923 + 0.889848I
b = 0.225706 + 0.133500I
5.60153 − 1.95285I 0
u = −0.262827 + 1.109140I
a = 1.37071 + 0.63527I
b = −0.589466 − 1.268910I
−4.24260 + 0.78323I 0
u = −0.262827 − 1.109140I
a = 1.37071 − 0.63527I
b = −0.589466 + 1.268910I
−4.24260 − 0.78323I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.221896 + 1.118480I
a = 1.56356 + 0.80568I
b = −1.85917 + 0.96230I
−1.53941 − 4.91431I 0
u = 0.221896 − 1.118480I
a = 1.56356 − 0.80568I
b = −1.85917 − 0.96230I
−1.53941 + 4.91431I 0
u = −0.369450 + 1.082930I
a = 2.49514 − 1.02643I
b = −2.47687 − 1.23020I
−0.42845 − 3.16967I 0
u = −0.369450 − 1.082930I
a = 2.49514 + 1.02643I
b = −2.47687 + 1.23020I
−0.42845 + 3.16967I 0
u = −0.569938 + 0.993899I
a = 1.09937 − 1.19180I
b = −1.97370 + 0.70903I
3.70280 − 4.55573I 0
u = −0.569938 − 0.993899I
a = 1.09937 + 1.19180I
b = −1.97370 − 0.70903I
3.70280 + 4.55573I 0
u = 0.748986 + 0.407820I
a = −0.480885 + 0.870943I
b = −0.37660 − 1.42830I
11.56620 + 0.45635I 11.06607 + 0.I
u = 0.748986 − 0.407820I
a = −0.480885 − 0.870943I
b = −0.37660 + 1.42830I
11.56620 − 0.45635I 11.06607 + 0.I
u = 0.778413 + 0.347104I
a = 1.53231 − 0.92520I
b = 1.88927 + 1.75371I
9.3131 − 11.7252I 8.57374 + 6.35355I
u = 0.778413 − 0.347104I
a = 1.53231 + 0.92520I
b = 1.88927 − 1.75371I
9.3131 + 11.7252I 8.57374 − 6.35355I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.315560 + 1.106870I
a = −1.42389 + 1.07397I
b = 1.74345 + 0.21862I
−4.77116 − 0.94849I 0
u = −0.315560 − 1.106870I
a = −1.42389 − 1.07397I
b = 1.74345 − 0.21862I
−4.77116 + 0.94849I 0
u = 0.213591 + 1.138180I
a = −1.96700 − 1.45359I
b = 2.52993 − 0.48874I
4.60011 − 9.01545I 0
u = 0.213591 − 1.138180I
a = −1.96700 + 1.45359I
b = 2.52993 + 0.48874I
4.60011 + 9.01545I 0
u = 0.760256 + 0.350052I
a = −1.36106 + 1.24216I
b = −1.68581 − 1.35119I
3.04655 − 7.53533I 6.19828 + 6.38149I
u = 0.760256 − 0.350052I
a = −1.36106 − 1.24216I
b = −1.68581 + 1.35119I
3.04655 + 7.53533I 6.19828 − 6.38149I
u = −0.753467 + 0.360125I
a = 0.315596 + 0.812998I
b = 1.80023 + 0.41209I
5.62104 + 5.06307I 8.08124 − 3.45988I
u = −0.753467 − 0.360125I
a = 0.315596 − 0.812998I
b = 1.80023 − 0.41209I
5.62104 − 5.06307I 8.08124 + 3.45988I
u = 0.588886 + 0.589287I
a = 0.119119 − 0.479902I
b = −0.213662 − 0.077887I
1.24735 + 1.77929I 1.80719 − 3.90932I
u = 0.588886 − 0.589287I
a = 0.119119 + 0.479902I
b = −0.213662 + 0.077887I
1.24735 − 1.77929I 1.80719 + 3.90932I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.365943 + 1.110030I
a = −2.17570 + 0.77453I
b = 1.32158 − 1.60784I
−3.03399 + 5.10519I 0
u = 0.365943 − 1.110030I
a = −2.17570 − 0.77453I
b = 1.32158 + 1.60784I
−3.03399 − 5.10519I 0
u = −0.592518 + 1.012050I
a = −1.75490 + 0.87977I
b = 1.79457 + 0.04402I
10.88800 − 7.88085I 0
u = −0.592518 − 1.012050I
a = −1.75490 − 0.87977I
b = 1.79457 − 0.04402I
10.88800 + 7.88085I 0
u = 0.739620 + 0.367451I
a = 0.81565 − 1.38746I
b = 1.12462 + 1.01801I
3.99256 − 2.37735I 8.68126 + 0.82850I
u = 0.739620 − 0.367451I
a = 0.81565 + 1.38746I
b = 1.12462 − 1.01801I
3.99256 + 2.37735I 8.68126 − 0.82850I
u = −0.292606 + 1.147000I
a = 0.04570 − 2.16311I
b = −1.43780 + 1.64269I
−1.262360 + 0.354071I 0
u = −0.292606 − 1.147000I
a = 0.04570 + 2.16311I
b = −1.43780 − 1.64269I
−1.262360 − 0.354071I 0
u = −0.513022 + 1.078080I
a = 2.60896 − 1.03032I
b = −2.72963 − 1.51757I
0.51902 − 3.88340I 0
u = −0.513022 − 1.078080I
a = 2.60896 + 1.03032I
b = −2.72963 + 1.51757I
0.51902 + 3.88340I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.378007 + 1.137450I
a = 2.54195 − 1.50040I
b = −1.07175 + 2.63458I
2.75696 + 8.75209I 0
u = 0.378007 − 1.137450I
a = 2.54195 + 1.50040I
b = −1.07175 − 2.63458I
2.75696 − 8.75209I 0
u = −0.726884 + 0.327055I
a = −0.175604 − 0.552864I
b = −0.963217 − 0.358705I
0.03213 + 3.48727I 0.09979 − 3.51807I
u = −0.726884 − 0.327055I
a = −0.175604 + 0.552864I
b = −0.963217 + 0.358705I
0.03213 − 3.48727I 0.09979 + 3.51807I
u = 0.492912 + 1.098740I
a = −0.276756 − 1.149500I
b = 1.057510 − 0.086412I
−2.19619 + 2.34413I 0
u = 0.492912 − 1.098740I
a = −0.276756 + 1.149500I
b = 1.057510 + 0.086412I
−2.19619 − 2.34413I 0
u = −0.740692 + 0.260753I
a = −0.682792 + 0.699061I
b = −0.17383 + 1.62028I
2.94737 + 3.48509I 7.97157 − 3.26658I
u = −0.740692 − 0.260753I
a = −0.682792 − 0.699061I
b = −0.17383 − 1.62028I
2.94737 − 3.48509I 7.97157 + 3.26658I
u = 0.533025 + 1.091700I
a = 0.231274 + 0.125966I
b = 0.088154 + 0.910822I
0.00591 + 6.09039I 0
u = 0.533025 − 1.091700I
a = 0.231274 − 0.125966I
b = 0.088154 − 0.910822I
0.00591 − 6.09039I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.471451 + 1.127850I
a = 0.06424 + 2.13769I
b = −1.84014 − 0.92549I
3.38462 − 0.90680I 0
u = 0.471451 − 1.127850I
a = 0.06424 − 2.13769I
b = −1.84014 + 0.92549I
3.38462 + 0.90680I 0
u = −0.529411 + 1.112630I
a = −1.94763 + 0.22116I
b = 1.51267 + 1.55593I
−3.31999 − 6.57687I 0
u = −0.529411 − 1.112630I
a = −1.94763 − 0.22116I
b = 1.51267 − 1.55593I
−3.31999 + 6.57687I 0
u = 0.584215 + 1.095890I
a = 1.80943 − 0.62472I
b = −1.07548 + 1.36552I
9.53744 + 4.60201I 0
u = 0.584215 − 1.095890I
a = 1.80943 + 0.62472I
b = −1.07548 − 1.36552I
9.53744 − 4.60201I 0
u = 0.570247 + 1.109490I
a = −2.04471 − 0.48819I
b = 2.40512 − 0.98669I
1.81489 + 7.35611I 0
u = 0.570247 − 1.109490I
a = −2.04471 + 0.48819I
b = 2.40512 + 0.98669I
1.81489 − 7.35611I 0
u = −0.556363 + 1.118210I
a = 0.53625 − 1.33820I
b = −1.51557 + 0.38281I
−2.27116 − 8.37309I 0
u = −0.556363 − 1.118210I
a = 0.53625 + 1.33820I
b = −1.51557 − 0.38281I
−2.27116 + 8.37309I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.573094 + 1.115450I
a = −1.05265 + 2.20004I
b = 2.54641 − 0.41856I
3.40071 − 10.08470I 0
u = −0.573094 − 1.115450I
a = −1.05265 − 2.20004I
b = 2.54641 + 0.41856I
3.40071 + 10.08470I 0
u = 0.572512 + 1.120620I
a = 2.84572 + 0.67318I
b = −3.08287 + 1.82619I
0.78058 + 12.56920I 0
u = 0.572512 − 1.120620I
a = 2.84572 − 0.67318I
b = −3.08287 − 1.82619I
0.78058 − 12.56920I 0
u = −0.539813 + 1.137000I
a = 1.67664 + 1.34204I
b = 0.10446 − 2.41080I
0.40620 − 8.31043I 0
u = −0.539813 − 1.137000I
a = 1.67664 − 1.34204I
b = 0.10446 + 2.41080I
0.40620 + 8.31043I 0
u = 0.577402 + 1.127000I
a = −3.33632 − 0.48264I
b = 3.09505 − 2.51845I
7.0114 + 16.8219I 0
u = 0.577402 − 1.127000I
a = −3.33632 + 0.48264I
b = 3.09505 + 2.51845I
7.0114 − 16.8219I 0
u = −0.662305 + 0.275534I
a = 0.939373 + 0.065618I
b = 0.922265 − 0.830172I
−0.94991 + 1.96351I −0.70822 − 3.53700I
u = −0.662305 − 0.275534I
a = 0.939373 − 0.065618I
b = 0.922265 + 0.830172I
−0.94991 − 1.96351I −0.70822 + 3.53700I
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.623195 + 0.345378I
a = −0.746323 − 1.172680I
b = −0.1202310 + 0.0270876I
2.14060 − 1.51973I 7.99267 + 0.24534I
u = 0.623195 − 0.345378I
a = −0.746323 + 1.172680I
b = −0.1202310 − 0.0270876I
2.14060 + 1.51973I 7.99267 − 0.24534I
u = 0.674211 + 0.096747I
a = −0.774201 + 0.504331I
b = −0.92810 + 1.42121I
6.25590 + 5.13644I 6.36962 − 3.22236I
u = 0.674211 − 0.096747I
a = −0.774201 − 0.504331I
b = −0.92810 − 1.42121I
6.25590 − 5.13644I 6.36962 + 3.22236I
u = 0.345648 + 0.580502I
a = 0.922401 + 0.248417I
b = 0.013474 − 0.285135I
0.099541 + 1.296110I 1.20042 − 5.96166I
u = 0.345648 − 0.580502I
a = 0.922401 − 0.248417I
b = 0.013474 + 0.285135I
0.099541 − 1.296110I 1.20042 + 5.96166I
u = −0.521577 + 0.412128I
a = −1.55675 − 1.07315I
b = −1.19110 + 0.98238I
2.50079 − 0.40687I 6.49172 − 2.07727I
u = −0.521577 − 0.412128I
a = −1.55675 + 1.07315I
b = −1.19110 − 0.98238I
2.50079 + 0.40687I 6.49172 + 2.07727I
u = 0.583943 + 0.129243I
a = 0.692839 + 0.144322I
b = 0.557460 − 0.795599I
0.30851 + 1.80358I 2.83929 − 3.75868I
u = 0.583943 − 0.129243I
a = 0.692839 − 0.144322I
b = 0.557460 + 0.795599I
0.30851 − 1.80358I 2.83929 + 3.75868I
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.493714
a = −1.89949
b = −1.32964
2.48657 3.95840
15
II. I
u
2
= hb + u, −u
3
+ a − u + 1, u
4
+ u
2
− u + 1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
2
a
8
=
−u
3
+ u
2
− u + 1
−u
2
+ u − 1
a
10
=
u
3
+ u − 1
−u
a
5
=
1
u
2
a
11
=
u
3
+ u − 1
−u
a
12
=
u
3
− u
2
+ u − 1
u
2
− u + 1
a
9
=
u
2
−u
2
− 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −5u
3
− 4u
2
− u + 6
16
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
4
− 2u
3
+ 3u
2
− u + 1
c
2
, c
4
, c
12
u
4
+ u
2
+ u + 1
c
3
u
4
+ 3u
3
+ 4u
2
+ 3u + 2
c
5
, c
10
u
4
c
6
u
4
+ u
2
− u + 1
c
7
u
4
+ 2u
3
+ 3u
2
+ u + 1
c
8
, c
9
(u + 1)
4
c
11
(u − 1)
4
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
4
+ 2y
3
+ 7y
2
+ 5y + 1
c
2
, c
4
, c
6
c
12
y
4
+ 2y
3
+ 3y
2
+ y + 1
c
3
y
4
− y
3
+ 2y
2
+ 7y + 4
c
5
, c
10
y
4
c
8
, c
9
, c
11
(y −1)
4
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.547424 + 0.585652I
a = −0.851808 + 0.911292I
b = −0.547424 − 0.585652I
2.62503 + 1.39709I 7.62200 − 4.77865I
u = 0.547424 − 0.585652I
a = −0.851808 − 0.911292I
b = −0.547424 + 0.585652I
2.62503 − 1.39709I 7.62200 + 4.77865I
u = −0.547424 + 1.120870I
a = 0.351808 + 0.720342I
b = 0.547424 − 1.120870I
−0.98010 − 7.64338I 0.87800 + 5.79053I
u = −0.547424 − 1.120870I
a = 0.351808 − 0.720342I
b = 0.547424 + 1.120870I
−0.98010 + 7.64338I 0.87800 − 5.79053I
19
III. I
u
3
=
h−u
5
−u
4
−2u
3
−2u
2
+b−2u−1, u
4
+u
2
+a, u
6
+u
5
+2u
4
+2u
3
+2u
2
+2u+1i
(i) Arc colorings
a
2
=
0
u
a
7
=
1
0
a
6
=
1
u
2
a
3
=
u
u
3
+ u
a
4
=
−u
3
u
3
+ u
a
1
=
u
3
u
5
+ u
3
+ u
a
8
=
u
4
+ u
2
+ u + 1
−2u
5
− u
4
− 3u
3
− 2u
2
− 3u − 2
a
10
=
−u
4
− u
2
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 1
a
5
=
1
u
2
a
11
=
−u
4
− u
2
u
5
+ u
4
+ 2u
3
+ 2u
2
+ 2u + 1
a
12
=
−u
4
− u
2
− u − 1
2u
5
+ u
4
+ 3u
3
+ 2u
2
+ 3u + 2
a
9
=
u + 1
−u
5
− u
3
− u − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −u
4
− 5u
3
− u
2
− 4u + 1
20
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1
c
2
, c
4
, c
12
u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1
c
3
(u
3
− u
2
+ 1)
2
c
5
, c
10
u
6
c
6
u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1
c
7
u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1
c
8
, c
9
(u + 1)
6
c
11
(u − 1)
6
21
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
7
y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1
c
2
, c
4
, c
6
c
12
y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1
c
3
(y
3
− y
2
+ 2y −1)
2
c
5
, c
10
y
6
c
8
, c
9
, c
11
(y −1)
6
22
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 0.498832 + 1.001300I
a = 1.183530 + 0.507021I
b = −1.39861 + 0.80012I
1.37919 + 2.82812I 7.06955 − 2.21599I
u = 0.498832 − 1.001300I
a = 1.183530 − 0.507021I
b = −1.39861 − 0.80012I
1.37919 − 2.82812I 7.06955 + 2.21599I
u = −0.284920 + 1.115140I
a = 0.215080 − 0.841795I
b = −0.784920 + 0.841795I
−2.75839 −2.84423 + 0.27335I
u = −0.284920 − 1.115140I
a = 0.215080 + 0.841795I
b = −0.784920 − 0.841795I
−2.75839 −2.84423 − 0.27335I
u = −0.713912 + 0.305839I
a = −0.398606 + 0.800120I
b = 0.183526 + 0.507021I
1.37919 + 2.82812I 4.27468 − 2.61835I
u = −0.713912 − 0.305839I
a = −0.398606 − 0.800120I
b = 0.183526 − 0.507021I
1.37919 − 2.82812I 4.27468 + 2.61835I
23
IV. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
4
− 2u
3
+ 3u
2
− u + 1)(u
6
− 3u
5
+ 4u
4
− 2u
3
+ 1)
· (u
101
+ 48u
100
+ ··· + u − 1)
c
2
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
101
− 2u
100
+ ··· − 3u + 1)
c
3
(u
3
− u
2
+ 1)
2
(u
4
+ 3u
3
+ 4u
2
+ 3u + 2)
· (u
101
+ 2u
100
+ ··· + 12760u + 1480)
c
4
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
101
− 2u
100
+ ··· − 86401u + 194329)
c
5
, c
10
u
10
(u
101
− u
100
+ ··· − 1024u − 1024)
c
6
(u
4
+ u
2
− u + 1)(u
6
+ u
5
+ 2u
4
+ 2u
3
+ 2u
2
+ 2u + 1)
· (u
101
− 2u
100
+ ··· − 3u + 1)
c
7
(u
4
+ 2u
3
+ 3u
2
+ u + 1)(u
6
+ 3u
5
+ 4u
4
+ 2u
3
+ 1)
· (u
101
− 10u
100
+ ··· − 42087u + 6643)
c
8
, c
9
((u + 1)
10
)(u
101
+ 11u
100
+ ··· − 8u − 1)
c
11
((u − 1)
10
)(u
101
+ 11u
100
+ ··· − 8u − 1)
c
12
(u
4
+ u
2
+ u + 1)(u
6
− u
5
+ 2u
4
− 2u
3
+ 2u
2
− 2u + 1)
· (u
101
+ 12u
100
+ ··· + 3723u + 277)
24
V. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
101
+ 12y
100
+ ··· − 7y −1)
c
2
, c
6
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
101
+ 48y
100
+ ··· + y −1)
c
3
(y
3
− y
2
+ 2y −1)
2
(y
4
− y
3
+ 2y
2
+ 7y + 4)
· (y
101
− 24y
100
+ ··· + 111920400y −2190400)
c
4
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
101
− 48y
100
+ ··· − 26966856735y −37763760241)
c
5
, c
10
y
10
(y
101
+ 63y
100
+ ··· − 4718592y −1048576)
c
7
(y
4
+ 2y
3
+ 7y
2
+ 5y + 1)(y
6
− y
5
+ 4y
4
− 2y
3
+ 8y
2
+ 1)
· (y
101
+ 24y
100
+ ··· − 2017745343y −44129449)
c
8
, c
9
, c
11
((y −1)
10
)(y
101
− 99y
100
+ ··· − 132y
2
− 1)
c
12
(y
4
+ 2y
3
+ 3y
2
+ y + 1)(y
6
+ 3y
5
+ 4y
4
+ 2y
3
+ 1)
· (y
101
+ 12y
100
+ ··· + 194657y −76729)
25
